Equal volumes of molar hydrochloric acid and sulphuric acid are neutralized by dil. `NaOH` solution and `x` Kcal and `y` Kcal of heat are liberated respectively. Which of the following is true?

Options

A. (a) `x=y`
B. (b) `x=(1)/(2)y`
C. (c) `x=2y`
D. (d) None of the above

Explanation

To solve the question, we need to analyze the heat of neutralization for hydrochloric acid (HCl) and sulfuric acid (H2SO4) when they react with dilute NaOH.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- When HCl is neutralized by NaOH, the reaction is:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
- When H2SO4 is neutralized by NaOH, the reaction is:
\[ \text{H}_2\text{SO}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]

2. **Heat of Neutralization**:
- The heat released during the neutralization of HCl with NaOH is denoted as \( -x \) Kcal (where \( x \) is the heat of neutralization).
- The heat released during the neutralization of H2SO4 with NaOH is denoted as \( -y \) Kcal (where \( y \) is the heat of neutralization).

3. **Moles of Water Formed**:
- In the case of HCl, 1 mole of HCl reacts to form 1 mole of water.
- In the case of H2SO4, 1 mole of H2SO4 reacts to form 2 moles of water.

4. **Heat of Formation of Water**:
- The heat of neutralization is related to the heat of formation of water. The formation of water from H+ and OH- ions releases a certain amount of heat.
- For HCl, the heat of neutralization (which is the same as the heat of formation of 1 mole of water) is \( -x \).
- For H2SO4, since 2 moles of water are formed, the heat of neutralization can be considered as \( -y \), but since it forms 2 moles of water, we can express it as:
\[ -y = 2 \times \text{(heat of formation of 1 mole of water)} \]

5. **Relating x and y**:
- Since the heat of formation of 1 mole of water is the same in both cases, we can relate \( x \) and \( y \):
\[ -x = -\frac{y}{2} \]
- This simplifies to:
\[ x = \frac{y}{2} \]

6. **Conclusion**:
- From the above relationship, we conclude that the heat released during the neutralization of HCl is half that of the heat released during the neutralization of H2SO4.
- Therefore, the correct answer is:
\[ x = \frac{y}{2} \]

### Final Answer:
The correct option is **B: x is equal to half of y**.